Sec12.7 - Sec.12.7 Extreme Values and Saddle Points A local...

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Sec.12.7 Extreme Values and Saddle Points A local minimum is a point in the domain that yields the smallest function value in a small region of the domain about it. A local maximum is a point in the domain that yields the largest function value in a small region of the domain about it. In dealing with multi-variable functions we may have a third type of point in the domain, called a saddle point, which appears as a maximum in one direction and a minimum in another direction! If the extreme points discussed above have the smallest (largest) function value in the whole domain, we say we have an absolute minimum (maximum). If f has a local maximum or minimum at (a, b ) and the first order partials exist, then they must equal zero. ( , )0 ( , xy f a b and f a b == . An interior point (a, b) of the domain is called a critical point (stationary point) if both first partials equal zero or if one of the first partials does not exist.
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Sec12.7 - Sec.12.7 Extreme Values and Saddle Points A local...

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